#### Vol. 292, No. 1, 2018

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Meridional rank and bridge number for a class of links

### Michel Boileau, Yeonhee Jang and Richard Weidmann

Vol. 292 (2018), No. 1, 61–80
##### Abstract

We prove that links with meridional rank 3 whose 2-fold branched covers are graph manifolds are 3-bridge links. This gives a partial answer to a question by S. Cappell and J. Shaneson on the relation between the bridge numbers and meridional ranks of links. To prove this result, we also show that the meridional rank of any satellite knot is at least $4$.

##### Keywords
knot, link, bridge number, meridian, meridional rank, 2-fold branched cover, graph manifold
Primary: 57M25